Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values 0 and −1 [Pletyukhov et al., Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation, and fixes the mod(1) ambiguity appearing in the modern theory of polarization. In the present paper we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as a function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from −Nc to zero, where Nc is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so-called nearsightedness principle formulated by Kohn [Kohn, Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the hard-wall boundary and interface charges in one-dimensional single-channel continuum [S. Miles et al., Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [N. Müller et al., Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance xφ∈[0,L] (where L is a potential periodicity) is given by a perfectly linear function of xφ plus an integer-valued topological invariant I, the so-called boundary invariant. We provide two equivalent representations for I(xφ): the winding-number representation and the bound-state representation. The winding-number representation allows one to write I as a winding index of a particular functional of bulk Green's function. The corresponding integration contour is chosen in the complex frequency plane to encircle the occupied part of the spectrum residing on the real axis. In turn, in the bound-state representation, I is expressed through the sum of the winding number of the boundary Green's function and the number of bound states supported by the cavity of size xφ below the chemical potential. We observe that during a single cycle in the variation of xφ, the boundary invariant exhibits exactly ν downward jumps, each by a unit of electron charge, whenever ν energy bands are completely filled leading to the value I(L)=−ν. Additionally, for translationally invariant models interrupted by a localized impurity we derive the winding-number expression for the excess charge accumulated on the said impurity. We observe that the charge accumulated on a single repulsive impurity is restricted to the values −Nc,⋯,0, where Nc is the number of channels (spin or orbital components) in the system. For systems with weak potential amplitudes, we additionally develop Green's-function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation

Fully carbon metasurface: Absorbing coating in microwaves

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.The microwave-absorbing properties of a heterostructure consisting of an ordered monolayer of porous glassy carbon spheres were experimentally and theoretically investigated in the Ka-band (26–37 GHz) frequency range. The electromagnetic response of such a “moth-eye”-like all-carbon metasurface at a normal incidence angle was modelled on the basis of long-wave approximation. Modelling parameters in the Ka-band were used to estimate and predict the absorption properties of monolayers in free space in the range 1–40 GHz. Experimental and theoretical results demonstrate that a metasurface based on porous glassy carbon spheres is an inert, lightweight, compact, and perfectly absorbing material for designing new effective microwave absorbers in various practically used frequency ranges.The work was supported by Projects FP7-610875 (NAMICEMC, 2013-2017), H2020 RISE 734164 Graphene 3D, and FP7 IRSES project CANTOR (Grant No. FP7-612285). Sijin Li thanks the China Scholarship Council for the financial support under Grant No. 201406510029. Cameron Gallagher and Emma Burgess acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1)

Electromagnetic properties of polyurethane template-based carbon foams in Ka-band

International audienceThe electromagnetic (EM) properties of polyurethane template-based reticulated carbon foams were investigated in the 26-37 GHz microwave frequency range (Ka-band). It was experimentally proved that carbon foams of a thickness of 2 mm and a density of 22-55 mg cm(-3) are almost not transparent to microwave radiation, and this is especially true for the densest ones. Depending on bulk density, the EM response of carbon foams in the microwave region can be mainly accounted for by either reflection or absorption. EM shielding efficiency of more dilute samples is due to absorption mechanisms, whereas denser foams provide up to 80% reflection of EM signals. EM properties of carbon foams in the Ka-band can be accurately predicted by a very simple model based on Fresnel formulae developed in this communication

Electromagnetic properties of polyurethane template-based carbon foams in Ka-band

The electromagnetic (EM) properties of polyurethane template-based reticulated carbon foams were investigated in the 26–37 GHz microwave frequency range (Ka-band). It was experimentally proved that carbon foams of a thickness of 2 mm and a density of 22–55 mg cm−3 are almost not transparent to microwave radiation, and this is especially true for the densest ones. Depending on bulk density, the EM response of carbon foams in the microwave region can be mainly accounted for by either reflection or absorption. EM shielding efficiency of more dilute samples is due to absorption mechanisms, whereas denser foams provide up to 80% reflection of EM signals. EM properties of carbon foams in the Ka-band can be accurately predicted by a very simple model based on Fresnel formulae developed in this communication

Fully carbon metasurface: Absorbing coating in microwaves

The microwave-absorbing properties of a heterostructure consisting of an ordered monolayer of porous glassy carbon spheres were experimentally and theoretically investigated in the Ka-band (26–37 GHz) frequency range. The electromagnetic response of such a “moth-eye”-like all-carbon metasurface at a normal incidence angle was modelled on the basis of long-wave approximation. Modelling parameters in the Ka-band were used to estimate and predict the absorption properties of monolayers in free space in the range 1–40 GHz. Experimental and theoretical results demonstrate that a metasurface based on porous glassy carbon spheres is an inert, lightweight, compact, and perfectly absorbing material for designing new effective microwave absorbers in various practically used frequency ranges